Here is the table of published estimates from my 2010 sauropod-history paper, augmented with the two more recent estimates extrapolated from limb-bone measurements:

Author and date

Method

Volume (l)

Density (kg/l)

Mass (kg)

Janensch (1938)

Not specified

—

—

`40 t’

Colbert (1962)

Displacement of sand

86,953

0.9

78,258

Russell et al. (1980)

Limb-bone allometry

—

—

13,618

Anderson et al. (1985)

Limb-bone allometry

—

—

29,000

Paul (1988)

Displacement of water

36,585

0.861

31,500

Alexander (1989)

Weighing in air and water

46,600

1.0

46,600

Gunga et al. (1995)

Computer model

74,420

1.0

74,420

Christiansen (1997)

Weighing in air and water

41,556

0.9

37,400

Henderson (2004)

Computer model

32,398

0.796

25,789

Henderson (2006)

Computer model

—

—

25,922

Gunga et al. (2008)

Computer model

47,600

0.8

38,000

Taylor (2009)

Graphic double integration

29,171

0.8

23,337

Campione and Evans (2012)

Limb-bone allometry

—

—

35,780

Benson et al. (2014)

Limb-bone allometry

—

—

34,000

(The estimate of Russell et al. (1980) is sometimes reported as 14900 kg. However, they report their estimate only as “14.9 t”; and since they also cite “the generally accepted figure of 85 tons”, which can only be a reference to Colbert (1962)”, we must assume that Russell et al. were using US tons throughout.)

The first thing to notice is that there is no very clear trend through time, either upwards or downwards. Here’s a plot of mass (y-axis) against year of estimate (x-axis):

I’ve not even tried to put a regression line through this: the outliers are so extreme they’d render it pretty much useless.

In fact, the lowest and highest estimates differ by a factor of 5.75, which is plainly absurd.

But we can go some way to fixing this by discarding the outliers. We can dump Colbert (1962) and Alexander (1989) as they used overweight toys as their references. We more or less have to dump Russell et al. (1980) simply because it’s impossible to take seriously. (Yes, this is the argument from personal incredulity, and I don’t feel good about it; but as Pual (1988) put it, “so little flesh simply cannot be stretched over the animal’s great frame”.) And we can ignore Gunga et al. (1995) because it used circular conic sections — a bug fixed by Gunga et al. (2008) by using elliptical sections.

With these four unpalatable outliers discarded, our highest and lowest estimates are those of Gunga et al. (2008) at 38,000 kg and Taylor (2009)at 23,337. The former should be taken seriously as it was done using photogrammetrical measurements of the actual skeletal mount. And so should the latter because Hurlburt (1999) showed that GDI is generally the least inaccurate of our mass-estimation techniques. That still gives us a factor of 1.63. That’s the difference between a lightweight 66 kg man and and overweight 108 kg.

Here’s another way of thinking about that 1.63 factor. Assuming two people are the same height, one of them weighing 1.62 times as much as the other means he has to be 1.28 times as wide and deep as the first (1.28^2 = 1.63). Here is a man next to his 1.28-times-as-wide equivalent:

I would call that a very noticeable difference. You wouldn’t expect someone estimating the mass of one of these men to come up with that of the other.

So what’s going on here? I truly don’t know. We are, let’s not forget, dealing with a complete skeletal mount here, one of the very best sauropod specimens in the world, which has been extensively studied for a century. Yet even within the last six years, we’re getting masses that vary by as much as the two dudes above.

June 2, 2014

Way back in November 2011, I got this inquiry from Keiron Pim:

I’m currently writing a popular guide to dinosaurs, to be published by Random House next autumn [Ed.: available now at amazon.com and at amazon.co.uk]. I’ve been writing about [Brachiosaurus and Giraffatitan], and have read your 2009 study vindicating the proposal to separate them into two genera.

[…]

I know you consider Brachiosaurus likely to have been bigger (and note that the specimen was not fully grown), with a longer trunk and tail – but most of the sources I can find give both animals the same body length, generally around 26m. Presumably this doesn’t reflect your work, and your calculations are different.

I replied at the time, and said that I’d post that response here on SV-POW!. But one thing and another prevented me from getting around to it, and I forgot all about it until recently. Since we’re currently in a sequence of Brachiosaurus-themed posts [part 1, part 2, part 3, part 4, part 5, part 6], this seems like a good time to fix that. So here is my response, fresh from November 2011, lightly edited.

Well, Giraffatitan has only been recognised as a separate animal at all in the last couple of years, and nearly everything that has been written about “Brachiosaurus“, at least in the technical literature, is actually about Giraffatitan. So existing sources that give the same length for both are probably not making a meaningful distinction between the two animals.

First, on Giraffatitan: Janensch (1950b:102) did a great job of measuring his composite mounted skeleton. His figure for the total length of Giraffatitan along the neural canal is 22.46 m, and is certainly the best estimate in the literature for an actual brachiosaur specimen (and quite possibly the best for any sauropod).

I don’t know where the figure of 26 m comes from, but as Janensch (1961:213) notes, the isolated fibula XV2 of Giraffatitan in the Berlin collection is 134 cm long, compared with 119 cm for that of the mounted skeleton. This is 1.126 times as long, which if scaled isometrically would yield a total length of 25.29 m. So that is defensible, but 26 m is not, really.

I would advise sticking with Janensch’s published figure of 22.46 m, as it’s based on good material, and also because it forms the basis of my comparative estimate for a Brachiosaurus of similar limb length.

Now in my 2009 paper I estimated with reasonable rigour that the torso of Brachiosaurus was probably about 23% longer than that of Giraffatitan, yielding 4.82 m rather than 3.92 that Janensch gave for Giraffatitan. On much less solid evidence, I tentatively estimated that the tail of Brachiosaurus might have been 20-25% longer than that of Giraffatitan. Given the paucity of evidence I would play safer by going with the lower end of that estimate, which would give a tail length of 9.14 m compared with Janensch’s 7.62 for Giraffatitan. Riggs (1904) tells us that the sacrum of Brachiosaurus is 0.95 m long, which is slightly less than 1.07 m for Giraffatitan. Finally, since we know nothing of the head and neck of Brachiosaurus, the null hypothesis has to be that they were similar in proportion to those of Giraffatitan.

Putting it all together, Brachiosaurus may have been longer in the torso by 0.9 m, and in the tail by 1.52 m, but shorter in the sacrum by 0.12 m — for a total additional length of 2.3 m. That would make Brachiosaurus 24.76 m long, which is 10% longer than Giraffatitan.

Note that all the Brachiosaurus figures are given with much greater precision than the sparse data we have really allows. I think you could round Janensch’s 22.46 m for Giraffatitan to 22.5 and be pretty confident in that number, but you shouldn’t really say anything more precise than “maybe about 25 m” for Brachiosaurus.

Finally, you correctly note that the Brachiosaurus specimen was not fully grown — we can tell because its coracoid was not fused to the scapula. But the same is true of the mounted Giraffatitan, so these two very similarly sized animals were both subadult. How much bigger did they get? We know from the fibula that Giraffatitan got at least 12-13% bigger than the well-known specimen, and I’d be pretty happy guessing the same about Brachiosaurus. And I wouldn’t rule out much bigger specimens, either.

May 19, 2014

You’ve probably seen a lot of yapping in the news about a new “world’s largest dinosaur”, with the standard photos of people lying down next to unfeasibly large bones. Here’s my favorite–various versions of it have been making the rounds, but I grabbed this one from Nima’s post on his blog, The Paleo King.

The first point I need to make here is that photos like these are attention-grabbing but they don’t really tell you much. Partly because they’re hard to interpret, and partly because they almost always look more impressive than they really are. For example, I am 6’2″ tall (1.88 meters). If I lie down next to a bone that is 7’2″ (219 cm) 6’8″ (203 cm) long, it is going to look ungodly huge–a full half a foot longer than I am tall. But that is the length of the femur of the Brachiosaurus holotype–we’ve known of sauropod femora that big for a century now. People get tripped up by this sort of thing all the time–even scientists. Update: even me! Somehow I had gotten it into my head that the Brachiosaurus femur was 219 cm, when it is actually 203 cm. That goof doesn’t affect any of what follows, because from here on down I used Argentinosaurus as the point of reference.

Second point: at least some of the reporting on this new find has been unusually–and refreshingly–nuanced. The first news story I read about it was this one, which gives Paul Barrett plenty of airtime to explain why we should be cautious about jumping to any conclusions regarding the size of the new animal. That will turn out to be prophetic.

But let’s get back to that photo. Just eyeballing it, it looks like the femur is about half again as long as the dude is tall (the dude, BTW, is Pablo Puerta, for whom Puertasaurus is named). I was reading Nima’s post and he guessed that the femur was in the neighborhood of 3 meters, which would be a significant size increase over the next-biggest sauropod known from fossils that still exist (i.e., not including semi-apocraphyal gigapods like Amphicoelias fragillimus and Bruhathkayosaurus). The current based-on-existing-fossils record-holder is Argentinosaurus–there is a partial femur that would have been about 2.5 meters long when complete. So a 3-meter femur would be a wonderful thing. But alas, it just ain’t so–or at least the one in the photo isn’t anywhere near that big. Allow me to demonstrate.

Here’s another copy of the photo with some measurements applied. There is no actual scale bar in the picture, but we can use the dimensions of the things we can see to figure some stuff out.

For starters, there is a lot of perspective distortion going on here. Pallet B is 350 pixels wide at the near end, 280 pixels at the far end–a difference of 20%. I didn’t put the far-end measurement for Pallet A into the picture, but from corner to corner it is 295 pixels.

Shipping pallets vary in size around the world, but in the US the most common size is 48 x 40 inches. Other countries use different sizes, mostly smaller; I am unaware of any standard shipping pallets larger than 48×40. So assuming that the ones in the picture are that size is actually a liberal assumption that will lead to large estimates–if the pallets are smaller than 48×40, then all of the dimensions I’m about to calculate will be smaller as well. Obviously the pallets have their narrow ends facing us, which is nice because 40 inches is almost exactly 1 meter. So we can divide other things in the picture by pallet length and get their dimensions in meters.

The near side of the femur is pretty much in line with the stringer running left-to-right down the middle of Pallet A. From the measurements of the ends of that pallet, we’d expect the middle-distance width to be about 330 pixels, and in fact I got 335. The 830-pixel line I drew on the near side is not the total length of the bone–you could add a bit more for the femoral head, to a max of maybe 860 or 870 pixels. Divide that by 335 and you get a max length of about 2.6 meters.

The 800-pixel line for the far side of the femur goes from the top of the head to the bottom of the medial condyle, so there’s no extending needed there. That line is at about the mid-point of Pallet B, or about 315 pixels. If Pallet B is a meter wide, the femur is 2.5 meters long.

We can also check things by trying to figure out how tall Pablo Puerta is. At first that looks more encouraging for the possibility that this is a record-breaker. If we assume the femur really is 3 meters long, and compare the 800-pixel femur line to the 500-pixel Pablo line, Pablo is 62.5% the length of the femur, or 1.87 meters–about the same height as me. That would be pretty tall for an Argentinian, but it’s certainly plausible.

But that’s not a legit comparison, because Pablo is farther from the camera than is the femur. Look at Pallet A–we can use the slats as perspective guides to help figure out where the proximal end of the femur ought to be if projected back to Pablo’s distance from the camera. If we do that at both ends, the length of the femur if placed where Pablo is lying would be 750 pixels or fewer, which would make Pablo at least 2 meters tall. People get a lot taller than that, but it would make him unusually tall, and if you’re trying to emphasize how big your sauropod is, you probably won’t pick the tallest person in the room to pull a Jensen. If we assume Pablo’s about 5’8″–average height for an Argentinian male–then the femur is about 2.6 meters long, which is consistent with the estimates from the pallets. He could well be shorter, in which the case the femur might also be shorter.

There are of course vast amounts of uncertainty in all of this. I have heard the number 2.4 meters thrown around in the media, which is within the margin of error of my crude estimates here–I deliberately skewed large at most decision points to give the hypothesized 3-meter femur the best possible chance. I have to emphasize that this is not how you do science–I’m deliberately doing this quick and dirty. But even using these admittedly flawed and somewhat goofy methods, it’s easy to show that the femur isn’t 3 meters long, or anywhere near it.

So, three last points:

As the post title implies, the new Argentine titanosaur is about the same size as Argentinosaurus. That shouldn’t be too surprising, since the mass estimates that have been quoted in the media are within a few percent of the mass estimates for Argentinosaurus. The new critter might be a hair bigger, but it doesn’t “smash” the record, and when we get actual measurements it could end up being smaller than Argentinosaurus in linear dimensions. I note that the size trumpeted in the media is a mass estimate based on femoral fatness, not femoral length. You’d think that if the biggest femur was demonstrably longer than the 2.5-meter Argentinosaurus femur, they’d lead with that. So the reporting so far is also consistent with an animal about the same size as Argentinosaurus.

That is in no way a disappointing result! That biggest Argentinosaurus femur is incomplete, so the 2.5-meter length is an estimate. Even if the big femur shown here is only (only!) 2.4 meters long, it’s still the longest complete limb bone from anything, ever. And even if the new animal is identical to Argentinosaurus in size, there’s still a lot more of it, so we’ll get a better idea of what these super-gigantic titanosaurs looked like. That’s a big win.

Finally, this is not a case of MYDD. There’s no paper yet, and I don’t blame the team for not making the measurements public until the work is done. I also don’t blame them for publicizing the find. So far, this seems to be exactly what they’re saying it is–an animal about the size of Argentinosaurus, and maybe just a hair bigger. That’s cool. I wish them the best of luck writing it up. I almost wrote “I can’t wait to see the paper” but actually I can–something like this, I’d rather they take their time and do it right. It may not be a record-smasher, but it’s a solid, incremental advance, and science needs those, too.

The rib-cage is tiny. It doesn’t even extend as far laterally as the position of the limb bones.

(And lest you think this is an oddity, do go and look at any mounted elephant skeleton of your choice, Indian or African. They’re all like this.)

What’s going on here?

Is Oxford’s elephant skeleton mounted incorrectly? More to the point, are all museums mounting their elephants incorrectly? Do elephants’ ribs project much more laterally in life?

Do elephants have a lot of body mass superficial to the rib-cage? If so, what is that mass? It’s hard to imagine they need a huge amount of muscle mass there, and it can’t be guts. Photos like this one, from the RVC’s televised elephant dissection on Inside Nature’s Giants, suggest the ribs are very close to the body surface:

I’m really not sure how to account for the discrepancy.

Were sauropods similarly much fatter than their mounted skeletons suggest? Either because we’re mounting their skeletons wrongly with the ribs too vertical, or because they had a lot of superficial body mass?

March 24, 2013

Here’s an update from the road–get ready for some crappy raw images, because that’s all I have the time or energy to post (with one exception).

Here’s OMNH 1331. It’s just the slightly convex articular end off a big vertebra, collected near Kenton, Oklahoma, in 1930s by one of J. Willis Stovall’s field crews. I measured the preserved width at 45 cm using a tape measure, and at 44.5 in GIMP using the scale bar in the photo, which is up on a piece of styrofoam so it’s about the same distance from the camera as the rim of the vertebra (i.e, about 8 feet–as high as I could get and still shoot straight down). So whether your distrust runs to tape measures or scale bars in photos, I am prepared to argue that this sucker is roughly 45 cm wide.

There’s admittedly not a ton of morphology here, but the size and the fact that the other side is hollow and has a midline bony septum show that it is a pneumatic vertebra from a sauropod, and given that the quarry it’s from was chock-full of Apatosaurus, and liberally salted with gigantic Apatosaurus, I feel pretty good about calling it Apatosaurus.

To figure out how wide the articular face was when it was intact, I duplicated the image and reversed it left-to-right in GIMP, which yields an intact max width of about 49 cm. That is friggin’ immense.

If we make the maximally conservative assumption that this is the largest centrum in the whole skeleton of a big Apatosaurus, then it has to be part of a dorsal vertebra. Here are the max diameters of the largest dorsal centra in some big mounted apatosaurs, taken from Gilmore (1936). The number in parentheses is how many percent bigger OMNH 1331 is.

A. louisae CM 3018 – 36.5 cm (34%)

A. parvus UWGM 15556 – 36.5 cm (34%)

A. sp. FMNH P25112 – 41 cm (20%)

However, this might not be part of a dorsal vertebra. For one thing, it’s pretty convex, and Apatosaurus dorsals sometimes have a little bump but they’re pretty close to amphiplatyan, at least in the posterior half of the series. For another, I think that smooth lower margin on the right in the photo above is part of the rim of a big pneumatic foramen, but it’s waaay up high and pretty medial on the centrum, opening more dorsally than laterally, which I have seen a lot in anterior caudal vertebrae. Finally, Jack McIntosh went through the OMNH collections years ago and his identifications formed the basis for a lot of the catalogue IDs, and this thing is catalogued as the condyle off the back end of a proximal caudal.

Here are the max diameters of the largest caudal centra in those same mounted apatosaurs, again taken from Gilmore (1936). Once again, the number in parentheses is how many percent bigger OMNH 1331 is.

A. louisae CM 3018 – 30 cm (63%)

A. parvus UWGM 15556 – 32.5 cm (51%)

A. sp. FMNH P25112 – 39 cm (26%)

(Aside: check out the skinny rear end on A. louisae. ‘Sup with that?)

So whatever vert it’s part of, OMNH 1331 is damn big bone from a damn big Apatosaurus. There are lots of other big Apatosaurus vertebrae in the OMNH collections, like OMNH 1670, but OMNH 1331 is the largest centrum that I know of in this museum. Which is why you’re getting a post about most of one end of a centrum in the wee hours of the morning–it’s most of one end of an awesome centrum. And it pains me when people do comparison figures of big sauropod vertebrae, or lists of the “Top 10 Largest Sauropods”, and put in stuff like Argentinosaurus and Puertasaurus and Supersaurus, but leave out Apatosaurus. It was legitimately huge, and it’s time the world realized that.

March 13, 2013

At the top: our old friend BYU 9024 — the cervical vertebra that’s part of the Supersaurus vivianae holotype. At the bottom, C2 (the longest cervical) of Giraffa camelopardalis angolensis FMNH 34426.

The Supersaurus vertebra is 138 cm long. We don’t know which cervical it is, but there’s no reason to think it’s the longest. The giraffe vertebra is 31 cm long. Not only is the Supersaurus vertebra four times as long as that of the giraffe, it’s one of more than twice as many cervicals as the giraffe has.

Did we cheat by using an unusually small giraffe? Not really. When we articulated all seven cervicals as best we could, the sequence measured 171 cm, which is a fairly healthy 71% of the 2.4 m neck of the world-record giraffe. It’s not a monster, but it’s a decent-sized adult.

March 3, 2013

If you’re just joining us, this post is a follow-up to this one, in which I considered the possible size and identity of the Recapture Creek femur fragment, which “Dinosaur Jim” Jensen (1987: page 604) said was “the largest bone I have ever seen”.

True to his word, Brooks Britt at BYU got back to me with measurements of the Recapture Creek femur fragment in practically no time at all:

Length 1035 mm, width 665 mm. However, you cannot trust the measurements because Jensen put a lot of plaster on the proximal half of the bone.

Now, taking plaster off a bone is not going to make it any larger. So the plastered-up specimen is the best case scenario for the RC femur to represent a gigapod. And I know the stated width of 665 mm is the max width of the proximal end, because I sent Brooks a diagram showing the measurements I was requesting. The length is a little less than anticipated, and doesn’t quite jibe with the max proximal width–I suspect a little might have broken off from the distal end where the preservation looks not-so-hot.

Based on those measurements, it looks like Jensen got the scale bar in Figure 8 in his 1987 paper approximately right–if anything, the scale bar is a little undersized, but only by 5% or so, which is actually pretty good as these things go (scale bars without measurements are still dag-nasty evil, though). By overlapping Jensen’s photo with the femur of the Brachiosaurus altithorax holotype (FMNH P25107) to estimate the size of the element when complete, I get a total length of 2.2 meters–exactly the same size as about 8% bigger than the Brachiosaurus holotype (actual length 2.03 m). If the Recapture Creek femur is from a Camarasaurus, which I don’t think we can rule out, it was 2 meters long when complete, or 11% longer and 37% more massive than the big C. supremus AMNH 5761–about 35 tonnes or maybe 40 on the outside. So it’s a big bone to be sure, but it doesn’t extend only slightly extends the known size range of Morrison sauropods. (Updated 2014-05-19–as I related in the first post, I somehow got it fixed in my head that the holotype B.a. femur was 2.19 m when it is actually 2.03 m.)

Now, here’s a weird thing. Let’s assume for the sake of this discussion that the Recapture Creek femur is from a brachiosaur. That gives us three individual Late Jurassic brachiosaurids–the Recapture Creek animal, the Brachiosaurus altithorax holotype, and the mounted Giraffatitan brancai–that are almost exactly the same size in limb bone dimensions (although B.a. had a longer torso). But we know that brachiosaurids got bigger, as evidenced by the XV2 specimen of Giraffatitan, and based on the lack of scapulocoracoid fusion in both FMNH P25107 and the mounted Giraffatitan. So why do we keep finding these (and smaller) subadults, and so few that were XV2-sized? I know that there gets to be a preservation bias against immense animals (it’s hard to bury a 50-tonne animal all in one go), but I would not think the 13% linear difference between these subadults and XV2-class adults would be enough to matter. Your thoughts?